I would attribute most of the issues early on to a significant lack of Cavalry Reconnaissance capabilities.

First Bull Run was very much the fault of inexperienced troops, and little to no trained field commanders (ie Captains, Colonels, etc).

But McClellan's major faults can be traced to inaccurate reports, and little to no cavalry screens and reconnaissance parties. Most of his timidity was due to him holding the belief that he was outnumbered, and thus shouldn't commit costly assaults, as far away as he was from meaningful supply and lines of retreat. He managed to maneuver himself into a corner in both of his two major engagements.

Pope walked into a trap at Second Bull Run, and Hooker may or may not have had a massive concussion that altered his ability to command effectively.

Burnside is really the only (major) commander that could be considered inept, or incompetent, at least in my opinion. If McClellan/Pope/Whomever had the Cavalry Corps of Late 1863 onwards, and if Stoneman had kept his position with Hookers' army and not gone off on his raid, I'd wager that their respective failures would turn out differently. Once Grant came into the theater, it was fairly obvious what Lee's military capabilities were, and Grant knew that as long as HE dictated the Operational Direction and Tempo, Lee would be forced to respond in kind. Sheridan being Sheridan, and the Union Cavalry Corps becoming incredibly competent didn't hurt.

To compare them to Taylor and Scott's armies in Mexico, both were very blessed to have significant investments in Cavalry, and Reconnaissance units. Much of Robert E Lee's early fame is his recon rides through 'impassible' lava beds to find flanking routes that led to significant victories at Cerro Gordo, Contreras, and Churubusco. Taylor had the renowned Texas Rangers, as well as several near-elite Dragoon companies to perform reconnaissance in their battles south.

In the Western Theater, Cavalry never achieved much of the same renown as their eastern counterparts. They were more often separated, and sent on independent missions, raid, harass, protect, etc, and not strictly intelligence gathering missions. And thanks to a near total lack of meaningful infrastructure in the West, Battles were very much planned out ahead of time, IE Nashville, Corinth, Jackson, Vicksburg, them being centered on vital supply lines, and the Confederacy being on the defensive almost 100% of the time. You don't really need to know where the enemy is, and what they are doing, when you know you have to defend/attack the railhub at X. Even Shiloh was dictated by Grant's necessity to halt, and defend Pittsburgh Landing, a steamboat/ferry dock.

As for WHY the Union didn't invest in their cavalry units early in the war, they were very VERY expensive to raise, and maintain. The logistics for cavalry forces are staggering. It was one of the largest expenditures for the Pre-War army, and a majority of their trained and skilled Cavalry Officer Corps defected to the south. Milita forces, and volunteers in the North weren't accustomed to riding horses, as they were in using them to plow fields, or drive carriages, which just increased the disparity of skill between Confederate Counter-Recon, or screening units, and Union Recon units.

I would start by arguing that the Union's generals were not incompetent, and that that narrative is mostly a product of the lost cause myth. Some of the most mocked and seemingly incompetent generals were actually fairly successful.

One of the common examples of Union incompetence is George McClellan, but was he really that incompetent? He failed to take Richmond and he was completely unable to use his vast numerical and material superiority, but he also had his successes. McClellan turned the fledgling Union army into a well trained and disciplined fighting force. He suffered numerous defeats, but when he met Lee at Antietam he achieved victory, though admittedly incomplete. Despite his failure to take Richmond, McClellan actually inflicted heavier casualties than he took in almost every engagement. Although McClellan failed to meet his goal, the casualties that he inflicted on the Confederate army would never be fully replaced.

Arguably nothing that happened under McClellan's command ended in "disaster." At no point was his army destroyed and usually casualties favored the Union. There is a long list of Union generals that are described as incompetent and inept, but their stories are usually similar.

The poor reputations of the Union's generals are mostly exaugurated, but so are the reputations of the Confederacy's generals. Men such as Robert Lee, Thomas Jackson, and J.E.B Stuart are remembered as incredibly skilled military geniuses. They were good generals, but their reputations are somewhat undeserved.

Lee was undoubtedly an exceptional commander, but he is responsible for some of the Confederacy's greatest defeats. Lee was driven back by McClellan at Antietam, and suffered comparable casualties to McClellan's forces. At Gettysburg Lee was responsible for Pickett's charge, which crippled his army for the rest of the war. Even Lee's successes, such as the 7 Days Battles, were marked by high casualties, often exceeding those of the Union army.

Lincoln's dissatisfaction with his generals stemmed from their inability to quickly win the war. The reputations of generals on both sides of the war are exaggerated, but Lincoln's expectations were unrealistic. Lincoln wanted a general who could march straight to Richmond and defeat the Confederate forces in full, and he was never able to find one. That does not mean that his generals were worse than their Confederate counterparts. After all, Lee was never able to reach Washington, and his invasion of Pennsylvania was far less successful than McClellan's campaigns. By 1863 Lincoln had come to terms with the fact that it would not be a short war, and so George Meade retained his post despite Lincoln's anger over his failure to destroy Lee at Gettysburg.

Lincoln was content with Grant's leadership because Grant was more aggressive than most of his predecessors. Grant was willing to sustain losses and continue pushing. Grant's aggressiveness fit Lincoln's vision of a decisive campaign to destroy the Confederacy, but was also incredibly costly. Most previous generals were unwilling to accept the losses that Grant was.

I have spent this entire post arguing that Confederate commanders were not superior to Union ones, but at the brigade and regimental levels they sometimes were. When the Confederacy seceded they took a large portion of the army with them, and none of its organization. What at first appears to be a disadvantage actually worked to the Confederacy's favor. The Union used the regular army alongside its volunteer forces, but the Confederacy had no regular army. This meant that former officers were distributed roughly evenly throughout the Confederate forces. Union regiments were often led by inexperienced men while Confederate regiments would have veterans and West Point veterans in command. To be clear, the Union did not lack skilled officers, on the contrary they had many more than the Confederacy. They simply did not utilize them as effectively because of the structure of the US army.

In order to evaluate the effectiveness of the Union's commanders, compare their successes and defeats to those of the Confederate commanders. What did Lee achieve that McClellan or Meade did not? McClellan failed to take Richmond, but Lee's attack into the north failed miserably, and McClellan's victory at Antietam was one of many turning points in the war.

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I have used George McClellan and Robert Lee as examples throughout this post, as they are two of the most famous generals of the war. The trend I described holds true for many other commanders as well.